10.04.11 12:04 AM ET

It looks like The Simpsons—20th Century Fox Television’s multibillion-dollar cash cow, the anchor of the Fox network’s Sunday primetime schedule, and the longest-running sitcom in the history of broadcasting—might stop production after the current 23rd season ends next spring.

The reason is a negotiating impasse between the studio and the six principal actors who voice the beloved characters on the animated series that hilariously satirizes middle-class Midwestern angst.

Difficult bargaining is nothing new for the show, which was created by James L. Brooks and Matt Groening. Fox studio execs have occasionally threatened to replace uncooperative cast members with sound-alike actors. But for the first time in nearly a quarter century of haggling, the executives have insisted that if the cast doesn’t accept a draconian 45 percent pay cut, The Simpsons will die an abrupt death as a first-run series.

A Fox Television spokesman had no comment at the time of publication Monday night. On Tuesday, the studio issued the following statement: "23 seasons in, The Simpsons is as creatively vibrant as ever and beloved by millions around the world. We believe this brilliant series can and should continue, but we cannot produce future seasons under its current financial model. We are hopeful that we can reach an agreement with the voice cast that allows The Simpsons to go on entertaining audiences with original episodes for many years to come."

The pay-cut ultimatum was delivered Monday evening as Fox spurned the actors’ proposal, delivered late last week, to take a cut of around 30 percent in exchange for a tiny percentage of the show’s huge back-end profits—amounting to untold billions—from syndication around the globe and merchandising of Simpsons clothing, lunchboxes, stamps, DVDs, a feature film, and videogames, among other paraphernalia. The series is produced by the 20th Century Fox studio and aired by the Fox network, both News Corp. companies, but the studio reaps the ancillary rewards.

“Fox is taking the position that unless they can cut the production costs really drastically, they’ll pull the plug on new shows,” said a Simpsons insider with knowledge of the negotiations. “The show has made billions in profits over the years and will continue to do so as far as the eye can see down the road. The actors are willing to take a pay cut of roughly a third, but that’s not good enough for Fox.”

Even under Fox Studio’s proposed downgrade, they would still be making around $4 million apiece, which goes a long way in the fictitious town of Springfield, and even in the allegedly real city of Hollywood.

But the actors have long argued that they deserve a taste of the plentiful syndication and merchandising profits because they’ve contributed creatively to the success of The Simpsons almost as much as Brooks and Groening. The latter two benefit greatly from the show’s back-end revenue, and will continue to get even richer off the second round of syndication deals once new episodes are no longer being produced.

But Fox has consistently refused to compensate the main cast members beyond their generous salaries, and once production ends, the studio will continue to reap billions for years to come (with Fox drawing on a valuable archive of around 500 episodes), while the actors will receive little more than their union-mandated residuals.

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“Now Fox is basically saying, ‘If you don’t take this deal, we’ll shut down the show,’ and they’ll continue to make a ton of money,” said the insider. “They’re free to sell it to cable and a second round of syndication, and they figure that the cast has very little leverage.”

The Simpsons—while no longer attracting the ratings it once did—remains the key to Fox’s Sunday-night schedule, serving as a strong 8 p.m. lead-in for Seth MacFarlane’s Family Guy and American Dad sitcoms.

“They’ve had plenty of opportunity to pick another show for 8 o’clock, and they haven’t done it,” said the insider.